Leetcode #650: 2 Keys Keyboard
In this guide, we solve Leetcode #650 2 Keys Keyboard in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is only one character 'A' on the screen of a notepad. You can perform one of two operations on this notepad for each step: Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Math, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: n = 3
Output: 3
Explanation: Initially, we have one character 'A'.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get 'AA'.
In step 3, we use Paste operation to get 'AAA'.
Python Solution
class Solution:
def minSteps(self, n: int) -> int:
def dfs(n):
if n == 1:
return 0
i, ans = 2, n
while i * i <= n:
if n % i == 0:
ans = min(ans, dfs(n // i) + i)
i += 1
return ans
return dfs(n)
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.